You should use the "Parent Company" field instead of the "Company Name" field to correctly associate your new contact with a company inside of Nimble.
When supplying a Parent Company, if it doesn't exist yet inside Nimble, it will get created.
If you want to map "person" fields using the New Contact trigger, you'll need to create a person in Nimble that doesn't have a company associated with them. Right now, if you create a person with a company, Nimble creates two records at the same time and sends first the person and then the company over the API, so in the editor you'll only see company record fields. Creating a sample person record with no company should get the person related fields you need to map the Zap.
If you are getting this error it is likely because you do not have any name field mapped on your action. To create a contact it will need at least one of the following: first name and/or last name for a person, company name for a company.